Simplify; express your answer in exponential form. Assume $n\neq 0, x\neq 0$. $\dfrac{{(n^{-1}x^{-4})^{-5}}}{{n^{2}x}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(n^{-1}x^{-4})^{-5} = (n^{-1})^{-5}(x^{-4})^{-5}}$ On the left, we have ${n^{-1}}$ to the exponent ${-5}$ . Now ${-1 \times -5 = 5}$ , so ${(n^{-1})^{-5} = n^{5}}$ Apply the ideas above to simplify the equation. $\dfrac{{(n^{-1}x^{-4})^{-5}}}{{n^{2}x}} = \dfrac{{n^{5}x^{20}}}{{n^{2}x}}$ Break up the equation by variable and simplify. $\dfrac{{n^{5}x^{20}}}{{n^{2}x}} = \dfrac{{n^{5}}}{{n^{2}}} \cdot \dfrac{{x^{20}}}{{x}} = n^{{5} - {2}} \cdot x^{{20} - {1}} = n^{3}x^{19}$